Significance test across multiple simulated experiments First time question on this site, so please bear with me, thank you:
I have 6 coin-flip-type experiments for which I can calculate 6 binomial p-values. I would now like to calculate the significance of observing at least 4 p-values < 0.05 in six experiments total.
In one approach, I used Fisher's method (http://en.wikipedia.org/wiki/Fishers_method) to compound the p-values, but I wanted to add an additional test based on simulating the original coin-flip data.
To this end, I performed random coin-flips (P=0.5) for each of the 6 experiments; the total number of flips differs between these 6 experiments but is irrelevant. I then count how many times (out of 100 simulations) the binomial p-value < 0.05. Simulating the original data 100 times, I get the following number of significant binomial p-values ("false positive hits") from these 6 experiments:
12, 13, 9, 10, 7, 11
Or divided by 100 (= frequency of false positive hits in simulated experiments):
0.12, 0.13, 0.09, 0.1, 0.07, 0.11
How do I calculate the probability that 4 or more out of these 6 would be positive given these frequencies? I realize that for calculating the probability that 6/6 are positive, I would simply multiply 0.12 x 0.13 x 0.09 x 0.1 x 0.07 x 0.11. But for 1-5/6 it's more complicated. I'm leaning towards a hypergeometric test, since I have to draw 6 times and I think there's no replacement, but I want to double-check with you experts.
Thank you! 
 A: I have a number of additional comments to make regarding issues I have with what you're describing (which I will come back to), but first let's just deal with the simple question:

I would now like to calculate the significance of observing at least 4 p-values < 0.05 in six experiments total.

By 'significance' I assume you mean 'probability of ... under the null'.
Simple version:
Imagine that the sample sizes were such that we could treat the distribution of p-values under the null as continuous. In that case they will be uniform under the null.
Then under $H_0$ each experiment has a 5% chance of giving a p-value below 0.05
The distribution of the number of experiments yielding p-values below 0.05 under the null is $\text{binomial}(6,0.05)$
Let $X\sim \text{binomial}(6,0.05)$. Then $P(X\geq 4) = 8.64\times 10^{-5}$
Less simple version:
The distribution of p-values is discrete, and a significance level of exactly 0.05 won't typically be attainable. A more accurate answer in this case involves finding the largest possible p-value less than 0.05 (which depends on the exact sample size for each experiment), and then doing a similar calculation for that case. It will give a smaller probability than the one I just calculated. This involves some slightly more complicated calculation, but it's perfectly possible to do it exactly, without simulation. 
(I don't think your simulation approach looks right, by the way, but since it's possible to do this question without worrying about that, I won't labor the point.)
